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Research of statics and free vibrations of cylindrical shells by not classic theory

Doan T.N., Firsanov V.V.

#### Abstract:

On basis of energy-consistent approach, we derive the motion equations of orthotropic shell with arbitrary geometry and the deflected mode that are presented by equations in three-dimensional elastic theory. Three-dimensional equations are reduced to two-dimensional ones by virtual displacements principle and the expansion of displacement components into polynomial series in the coordinate system, which is normal to the middle plane of the shell. The modified boundary conditions for standard cases of mounting shell are formulated. As an example, the paper considers static deformation and natural vibrations of a circular cylindrical shell. The equations of equilibrium in displacements and boundary conditions are presented. Calculation of shell’s deflected mode is carried out by using Laplace transform, and then the number of arbitrary constants in the integration of differential equations systems is halved. The values of natural frequencies are determined by Bubnov-Galerkin variational method. The effect of different types of boundary conditions on deflected mode and the values of natural frequencies are analyzed. The comparison between calculation results of the natural frequencies obtained in this work and those by some versions of the classical theory by Donnell-Mushtari, Goldenweiser-Novozhilov, as well as three-dimensional theory of elasticity is made. The received results can be used in calculations and at tests for strength and durability of aviation and space-rocket, and also engineering structures of different destination.

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